I agree with Derfred.
Why is the first (recall) item on the checklist an instruction to disengage the autopilot? Because much of the automation has potentially become as unreliable as the airspeed. It follows up by removing misleading guidance and possible interference from the FBW systems.
There is significant danger involved in applying non-SOP methods due to instant diagnoses. There are many manifestations of pitot/static failures and part-failures and they can be even more confusing when they happen in turbulence and/or shear (which is unfortunate, as this is a more likely scenario). Best to just follow the QRH unless you’re actually going to hit something.
As an aside, I’ve often thought it would be useful to have a guarded button that removed all displays of airspeed from the cockpit and informed the automation to disregard it. Half of the annoyance is getting warnings and/or undesirable behaviour triggered by something you know is wrong.